Thanks for providing these interesting details Torn!
The way I do it is similar to the friction bath but in effect quite different.
I would say it is a blend of the friction bath and the Karsai Nei Tsang, a Taoist practice involving massaging the genitals.
It is a kind of Karsai Nei Tsang with the value of cold water added. Not as thorough as Karsai Nei Tsang because you cannot do it to yourself completely, but you can do more than half the movements on your own.
And maybe more efficient in some ways than Karsai Nei Tsang because of the cold effect and because you can do it regularly, no need to go some place to find a qualified therapist, which is obviously not something you want to do on a regular basis. Apart from the unavailability of such a person.
An interesting difference is in the use of temperature. Karsai Nei Tsang uses hot compresses : maybe being traditional it comes from a time when there were no icecubes? Maybe the cold is efffective because it brings a renewal of blood with subsequent heat? So the ice cubes are actually heating?
One way or the other this is an area where temperature is extremely important, if only to conserve motility of sperm. So I suppose there must be some kind of feedback effect with the thyroid and the brain.
Both of the sitz baths recommended in that book you found carefully avoid the most important areas, or I would say avoid touching the important areas where most of the lymphatic knots are situated, reaching them only through the effect of cold water. No doubt that SIN is in mind.
More info on Karsai Nei Tsang :
There is an excellent book:
http://www.amazon.com/Karsai-Nei-Tsang-Therapeutic-Massage/dp/1594771146
I read the book and it is well illustrated and very clear.
Some videos also I think. Mantak Chia does produce a video.
The technique is known elsewhere as "Jap Kasai" when for men and "Yok Thong" or "Yokutong" for women. Apart from Mantak Chia in his Tao Garden, there is another school I know of teaching it and producing a video, this is NBS in Chiang Mai (Thailand).
Their video is in Japanese I think :
http://chiangmai-massage.com/english/dvd.html
I have not seen the videos. The excerpts on Youtube don't really show what it is about.
A lot of the gestures are done on the lines which are rubbed while doing the BD (Bains Dérivatifs) : the line from top of the hip to perineum. After reading the book I have changed my gestures from a simple to and fro movement to a progressive circular movement, small circles with pressure along those lines, broken every time I have to refresh the cloth. It seems to work better as I feel more activity under the scalp. Hair gets quite greasy very fast and I have to wash it more often, a sure sign of detox from the head. As well as red itchy patches that last one day behind the ears and at nape.
I hope this helps many.